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arXiv · 2412.15161

Geometric Properties and Distance Inequalities on Grassmannians

Tin-Yau Tam·Xiang Xiang Wang
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Abstract

In this paper we obtain inequalities for the geometric mean of elements in the Grassmannians. These inequalities reflect the elliptic geometry of the Grassmannians as Riemannian manifolds. These include Semi-Parallelogram Law, Law of Cosines and geodesic triangle inequalities.

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Tin-Yau Tam, Xiang Xiang Wang. 2024-12-19. Geometric Properties and Distance Inequalities on Grassmannians. https://arxiv.org/abs/2412.15161

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